Divergence and Deformed Exponential Family
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911338865885184 |
|---|---|
| author | Matsuzoe, Hiroshi Takatsu, Asuka |
| author_facet | Matsuzoe, Hiroshi Takatsu, Asuka |
| contents | The Kullback--Leibler divergence together with exponential families establishes the foundation of information geometry and is widely generalized. Among the generalization, we focus on the $(h,τ)$-divergence and $(h,τ)$-exponential families. We present a sufficient condition for the $(h,τ)$-divergence to induce a Hessian structure on an $(h,τ)$-exponential family. We also define the $(h,τ)$-dependence of random variables and prove a kind of the law of large numbers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_21532 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Divergence and Deformed Exponential Family Matsuzoe, Hiroshi Takatsu, Asuka Differential Geometry Probability 53B12, 62B11 The Kullback--Leibler divergence together with exponential families establishes the foundation of information geometry and is widely generalized. Among the generalization, we focus on the $(h,τ)$-divergence and $(h,τ)$-exponential families. We present a sufficient condition for the $(h,τ)$-divergence to induce a Hessian structure on an $(h,τ)$-exponential family. We also define the $(h,τ)$-dependence of random variables and prove a kind of the law of large numbers. |
| title | Divergence and Deformed Exponential Family |
| topic | Differential Geometry Probability 53B12, 62B11 |
| url | https://arxiv.org/abs/2512.21532 |